Fall 2024 - P3
3.5 Booleans; De Morgan's Law (Period 3)
Student led teaching on Booleans. Learn how booleans are used in decision-making with logical operators.
De Morgan’s Law
According to De Morgan’s first law, the complement of the union of two sets A and B is equal to the intersection of the complement of the sets A and B
Examples:
“I don’t like chocolate or vanilla” = “I do not like chocolate and I do not like vanilla”
In this example, both statements are logically the same
De Morgans Law in Code!
Javascript Example:
%%javascript
let x = 19;
let y = 50;
// ! means not. So !true is false.
// || means OR.
if (!(x > 20 || y > 20)) {
console.log("I am the same condition as the one below!")
//This will not be true since x is less than 20
}
// && means AND.
if (!(x > 20) && !(y > 20)) {
console.log("I am the same condition as the one above!")
//This will also not be true since x is less than 20
}
x = 50
y = 100
if (!(x < 20 || y < 20)) {
console.log("I will be true since both is also greater than 20 now!")
//This WILL be true since both variables are greater than 20
}
// && means AND.
if (!(x < 20) && !(y < 20)) {
console.log("I am the same condition as the one above!")
//This WILL be true since both variables are greater than 20
}
// In all, not(X OR Y) is the same as (not(x) AND not(Y))
<IPython.core.display.Javascript object>
Python Example:
x = 19
y = 50
if not (x > 20 or y > 20):
print("Im not gonna be true since X is less than 20")
# This will not be true since x is less than 20
if not (x > 20) and not (y > 20):
print("I am the same condition as the one above!")
# This will also not be true since x is less than 20
x = 50
y = 100
if not (x < 20 or y < 20):
print("I will be true since both x and y are greater than 20 now!")
# This WILL be true since both variables are greater than 20
if not (x < 20) and not (y < 20):
print("I will also be true since both x and y are greater than 20 now!")
# This WILL be true since both variables are greater than 20
# In all, not(X OR Y) is the same as (not(X) AND not(Y))
I will be true since both x and y are greater than 20 now!
I will also be true since both x and y are greater than 20 now!